Question

The Arizona Department of Transportation wishes to survey state residents to determine what proportion of the population would like to increase statewide highway speed to 75 from 65 mph. At least how many residents do they need to survey if they want to be at least 99% confident that the sample proportion is within 0.07 of the true proportion?

Answer 1

Answer: 339

Step-by-step explanation:

Since the prior estimate of population proportion is unknown , then we take p= 0.5

Given : Margin of error : E=0.07

Critical value for 99% confidence interval : $z_{\alpha/2}=2.576$

Formula for sample size :-

$n=0.5(1-0.5)(\dfrac{z_{\alpha/2}}{E})^2\\\\=0.25(\dfrac{2.576}{0.07})^2\\\\=338.56\approx339$

Hence, the minimum sample size required = 339

i.e. they need to survey 339 residents.